Exploring the use of a colouring task to elicit young students’ mathematical reasoning

In this paper, we present the results of a study investigating the reasoning processes of grade 3 students working collaboratively to solve a combinatorial task. The task, which involved colouring and identifying colour combinations, was designed to be playful, engaging, and at the same time meaningful for students of that age. Our analysis drew on six mathematical reasoning actions, adapted from existing frameworks: noticing similarities or relations, developing conjectures, generalising to identify commonalities, justifying based on already‑understood ideas, verifying that a common property holds for each member of a group, and generalising properties. We also employed an established framework for categorising solution strategies in combinatorial tasks, comprising four strategies: random selection of items without rejection of inappropriate items; trial-and-error involving random selection with rejection of inappropriate items; emerging patterns in item selection with rejection of inappropriate items; and consistent, complete cyclical patterns in item selection with rejection of inappropriate items. Our results show that the young students demonstrated a wide range of reasoning actions during their interactions, some of which attained the level of generalisation. All nine groups displayed at least three reasoning actions, while four groups demonstrated all six actions, thereby reaching the most advanced level of generalising properties. With respect to solution strategies, all groups progressed systematically from random selection to consistent and complete cyclical patterns. The reasoning actions developed cooperatively through student interaction, and all groups successfully solved the task by identifying all six possible colour combinations.